(A) Let the length of the ladder be the hypotenuse $h = 2.6 \,m$.Let the distance of the lower end from the wall be the base $b = 1 \,m$.Let the heigh

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(A) Let the length of the ladder be the hypotenuse $h = 2.6 \,m$.Let the distance of the lower end from the wall be the base $b = 1 \,m$.Let the height reached by the ladder on the wall be $a$.According to the Pythagorean theorem,$a^2 + b^2 = h^2$.Substituting the values: $a^2 + (1)^2 = (2.6)^2$.$a^2 + 1 = 6.76$.$a^2 = 6.76 - 1 = 5.76$.$a = \sqrt{5.76} = 2.4 \,m$.Thus,the upper end reaches a height of $2.4 \,m$ on the wall.

Class 10 Mathematics Triangles Mix Examples - Triangles

Medium

$A$ $2.6 \,m$ long ladder leans on a wall such that its lower end remains $1 \,m$ away from the base of the wall. Then,its upper end reaches to the height of .....$m$ on the wall.

A
$2.4$
B
$2$
C
$2.5$
D
$1.5$

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In $\Delta ABC$, $M$ and $N$ are the midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. If the area of $\Delta ABC$ is $90$, find the area of $\Delta AMN$.

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In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AD}$ is a median. If $AD = 12$ and $BC = 18$,then the area of $\Delta ABC$ is.............

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The perimeter of rhombus $ABCD$ is $116$. If $AC = 42$, find $BD$.

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In $\Delta ABC$,$m \angle B = 45^{\circ}$ and $\overline{AM}$ is an altitude,$M \in \overline{BC}$. If $BC = 7$ and $AM = 4$,then $AC = \ldots$

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In $\Delta ABC$,$P, Q$ and $R$ are the midpoints of $\overline{BC}, \overline{CA}$ and $\overline{AB}$ respectively. Then,$Area(BCQR) = \ldots \ldots \ldots \times Area(ABC)$.

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$A$ $2.6 \,m$ long ladder leans on a wall such that its lower end remains $1 \,m$ away from the base of the wall. Then,its upper end reaches to the height of .....$m$ on the wall.

Similar Questions

In $\Delta ABC$, $M$ and $N$ are the midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. If the area of $\Delta ABC$ is $90$, find the area of $\Delta AMN$.

In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AD}$ is a median. If $AD = 12$ and $BC = 18$,then the area of $\Delta ABC$ is.............

The perimeter of rhombus $ABCD$ is $116$. If $AC = 42$, find $BD$.

In $\Delta ABC$,$m \angle B = 45^{\circ}$ and $\overline{AM}$ is an altitude,$M \in \overline{BC}$. If $BC = 7$ and $AM = 4$,then $AC = \ldots$

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