Please help me answer this question on congruent triangles. 30 points

Question

asked Mar 25, 2023 134k views

1 Answer

Codnodder · Answer 1 · 2023-03-29T05:26:07+0000

Answer:

h = 24 cm

Explanation:

Let
= height of ΔCBD

Let
= height of ΔABE

As ΔABE ~ ΔCBD then AE : CD =
:

Given:

$\implies 20 : 10 = h : x$

$\implies (20)/(10)=(h)/(x)$

Cross multiply:

$\implies 20x=10h$

Simplify:

$\implies 2x=h$

As we are told that
$x+h=36 \ \sf cm$

$\implies h=36-x$

Equate the two equations for
and solve for
:

$\implies 2x=36-x$

$\implies 3x=36$

$\implies x=12$

Since
h=2x then

$\implies h=2 \cdot 12$

$\implies h=24 \ \sf cm$