Question

Solve for x.

Answers available are.
a.) 12.5
b.) 4√7
c.) 3√7
d.) 12

Answer 1

Answer:

d) 12

Step-by-step explanation:

Given:

Right triangle with side 9+7=16

let the third side of bigger triangle be y

and perpendicular line between 9 and 7 be z

Now:

By Pythagoras theorem:

(16)^2=x^2+y^2

x^2=256-y^2

Also

y^2=z^2 +7^2

z^2=y^2-49

and

x^2=9^2 + z^2

Now substituting z^2=y^2-49 in above we get:

x^2=81 + y^2-49

x^2=32+y^2

Adding x^2=256-y^2 and x^2=32+y^2 we get:

2x^2= 288

x^2=144

x=12 !

Answer 2

Answer:

The value of x is 12

Step-by-step explanation:

Let ABC is a triangle in which,

AB = x, BD = 9 unit, DC = 7 unit,

Where, D ∈ BC,

∵ ∠ABC ≅ ∠DBC ( common angles )

Also, ∠BAC ≅ ∠ADB ( right angles )

By AA similarity postulate,

$\triangle ABC\sim \triangle DBA$

∵ Corresponding sides of similar triangles are in same proportion,

$\implies \frac{AB}{BC}=\frac{DB}{AB}$

$\implies \frac{x}{9+7}=\frac{9}{x}$  ( ∵ BC = BC + DC )

$x^2 = 144$

$\implies x = 12$ ( Sides can not be negative )

Hence, the value of x is 12.