Question

In triangles △KHJ and △LGW, m∠K=m∠L, m∠H=m∠G, KH=8, LG=4, GW=2.5, and KJ=LW+3. Find the unknown sides of these triangles.

Answer 1

Answer:

KJ = 6 , LW = 3 , KJ = 6

Step-by-step explanation:

Let LW be x then KJ be x + 3

In ΔKHJ and ΔLGW,

∠K = ∠L and ∠H = ∠G , So, by AA Similarity, $\Delta KHJ \sim\Delta LGW$

Therefore,

$\frac{8}{4}=\frac{x+3}{x} =\frac{HJ}{2.5}$

First taking,

$\frac{8}{4}=\frac{x+3}{x}\\8\cdot x = 4\cdot x + 12\\4\cdot x=12\\x=3$

∴LW = 3 , KJ = 6

Now,

$\frac{8}{4}=\frac{HJ}{2.5}$

⇒ HJ = 5