(D) In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $\overline{AD}$ is an altitude to the hypotenuse $\overline{BC}$.According to the geometric mean the

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $\overline{AD}$ is an altitude to the hypotenuse $\overline{BC}$.According to the geometric mean theorem for right-angled triangles,$AB^{2} = BD \cdot BC$.Substituting the given values: $(\sqrt{5})^{2} = 2 \cdot BC$.$5 = 2 \cdot BC$.$BC = \frac{5}{2} = 2.5$.Therefore,the length of the hypotenuse $\overline{BC}$ is $2.5$.

Class 10 Mathematics Triangles Mix Examples - Triangles

Medium

In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $\overline{AD}$ is an altitude. If $AB = \sqrt{5}$ and $BD = 2$,then the length of hypotenuse $\overline{BC}$ is.........

A
$2\sqrt{5}$
B
$3$
C
$\sqrt{10}$
D
$2.5$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Triangles

Subtopic

Mix Examples - Triangles

In $\Delta ABC$,if $\ldots \ldots \ldots \ldots$,then by Apollonius' theorem,$AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})$ holds good.

Easy

View Solution

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $BM = 12$ and $AM = 9$,then $AC = \ldots$

Easy

View Solution

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overline{PQ} \parallel \overline{BC}$. If $AP = 8x-7$,$PB = 5x-3$,$AQ = 4x-3$ and $QC = 3x-1$,find the value of $x$.

Medium

View Solution

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $m \angle A = 60^{\circ}$. If $AC = 10$,then $AB = \dots$

Easy

View Solution

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QS}$ is an altitude to the hypotenuse $PR$. If $PQ = 6$ and $PS = 4$,find $QS$,$QR$,and $RS$.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In $\Delta ABC$,$m \angle A = 90^{\circ}$ and $\overline{AD}$ is an altitude. If $AB = \sqrt{5}$ and $BD = 2$,then the length of hypotenuse $\overline{BC}$ is.........

Similar Questions

In $\Delta ABC$,if $\ldots \ldots \ldots \ldots$,then by Apollonius' theorem,$AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})$ holds good.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $BM = 12$ and $AM = 9$,then $AC = \ldots$

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overline{PQ} \parallel \overline{BC}$. If $AP = 8x-7$,$PB = 5x-3$,$AQ = 4x-3$ and $QC = 3x-1$,find the value of $x$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $m \angle A = 60^{\circ}$. If $AC = 10$,then $AB = \dots$

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QS}$ is an altitude to the hypotenuse $PR$. If $PQ = 6$ and $PS = 4$,find $QS$,$QR$,and $RS$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module