In Delta PQR, the midpoints of the sides are | vedclass

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

Question

(A) According to the Midpoint Theorem,the triangle formed by joining the midpoints of the sides of a triangle divides the original triangle into four

Vedclass · Accepted Answer

Area of $\Delta XYZ = 60,$ Area of $\Delta ABC = 15$

Vedclass · Answer

(A) According to the Midpoint Theorem,the triangle formed by joining the midpoints of the sides of a triangle divides the original triangle into four congruent triangles,each having an area equal to $1/4$ of the original triangle.$1$. For $\Delta PQR,$ the midpoints are $X, Y, Z.$ Therefore,$	ext{Area}(\Delta XYZ) = \frac{1}{4} 	imes 	ext{Area}(\Delta PQR) = \frac{1}{4} 	imes 240 = 60.$$2$. Similarly,for $\Delta XYZ,$ the midpoints are $A, B, C.$ Therefore,$	ext{Area}(\Delta ABC) = \frac{1}{4} 	imes 	ext{Area}(\Delta XYZ) = \frac{1}{4} 	imes 60 = 15.$Thus,the area of $\Delta XYZ$ is $60$ and the area of $\Delta ABC$ is $15.$

In $\Delta PQR,$ the midpoints of the sides are $X, Y, Z.$ In $\Delta XYZ,$ the midpoints of the sides are $A, B, C.$ If the area of $\Delta PQR$ is $240,$ find the area of $\Delta XYZ$ and $\Delta ABC.$

Similar Questions

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude. If $QM = 6$ and $MR = 9$,then $PR = \ldots$

If in two triangles $DEF$ and $PQR$,$\angle D = \angle Q$ and $\angle R = \angle E$,then which of the following is not true?

In $\Delta ABC$,$D \in \overline{AB}$,$E \in \overline{AC}$ and $\overline{DE} \parallel \overline{BC}$. $F$ is a point on $\overline{AD}$ such that $\overline{EF} \parallel \overline{CD}$. Prove that $AD^2 = AB \times AF$.

In $\Delta XYZ$,$m \angle Y = 90^\circ$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $XM = 5$ and $ZM = 4$,find $YZ$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 4$ and $CM = 6$,then $BM = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module