(B) Let the length of the ladder be the hypotenuse $h = 4 \,m$.Let the height reached on the wall be the perpendicular $p = 3.2 \,m$.Let the distance

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(B) Let the length of the ladder be the hypotenuse $h = 4 \,m$.Let the height reached on the wall be the perpendicular $p = 3.2 \,m$.Let the distance between the base of the wall and the lower end of the ladder be the base $b$.According to the Pythagorean theorem,$h^2 = p^2 + b^2$.Substituting the values: $4^2 = (3.2)^2 + b^2$.$16 = 10.24 + b^2$.$b^2 = 16 - 10.24 = 5.76$.$b = \sqrt{5.76} = 2.4 \,m$.

Class 10 Mathematics Triangles Mix Examples - Triangles

Medium

$A$ $4 \,m$ long ladder leans on a wall to reach a height of $3.2 \,m$ on the wall. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

A
$0.9$
B
$2.4$
C
$3.2$
D
$4.1$

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In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AB = 20$ and $BC = 21$,find $BM$. (in $.5$)

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If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $AB = 5, BC = 7, AC = 10$ and $PR = 15$,the perimeter of $\Delta PQR$ is........

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

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In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $BM = 12$ and $CM = 18$,find $AB$.

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$A$ $4 \,m$ long ladder leans on a wall to reach a height of $3.2 \,m$ on the wall. Find the distance in $m$ between the lower end of the ladder and the base of the wall.

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In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AB = 20$ and $BC = 21$,find $BM$. (in $.5$)

$\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow EDF$. If $XY = 3, YZ = 4, ZX = 6$ and $DF = 12$,find the perimeter of $\Delta DEF$.

If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR$. If $AB = 5, BC = 7, AC = 10$ and $PR = 15$,the perimeter of $\Delta PQR$ is........

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