Question

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

Answer 1

Answer:

h = 24 cm

Step-by-step explanation:

Let $x$ = height of ΔCBD

Let $h$ = height of ΔABE

As ΔABE ~ ΔCBD then AE : CD = $h$ : $x$

Given:

• AE = 20 cm
• CD = 10 cm

$\implies 20 : 10 = h : x$

$\implies \dfrac{20}{10}=\dfrac{h}{x}$

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 $h$ and solve for $x$:

$\implies 2x=36-x$

$\implies 3x=36$

$\implies x=12$

Since $h=2x$ then

$\implies h=2 \cdot 12$

$\implies h=24 \ \sf cm$