Question

If the area of an isosceles right triangle is 8 cm, what is the perimeter of the triangle?
A. 8+ cm2
B. 8+4cm2
C. 4+8cm2
D. 12 cm2

Answer 1

Answer:

The perimeter of isosceles right Triangle is 8 + 4√2  cm

Step-by-step explanation:

Given as :

For isosceles right Triangle

The Area of isosceles right Triangle = A = 8 sq cm

Let , The measure of common side = a cm

The measure of uncommon side = h cm

Let The perimeter of isosceles right Triangle = P cm

According to question

Area = $\dfrac{1}{2}$ × base × height

i.e base × height = 2 × A

Or, base × height = 2 × 8

Or, b × b = 16 sq cm

i.e  b × b = 16 sq cm

Or,  b² =  16

i.e  b = √16 = 4 cm

So, measure of common side = b = 4 cm

∵ For right angle triangle

h = $\sqrt{a^{2}+b^{2} }$

Or, h = $\sqrt{4^{2}+4^{2} }$

Or, h = 4√2 cm

So, measure of uncommon side = h = 4√2  cm

Again

perimeter of isosceles right Triangle = ( 2 b + h ) cm

i.e P = 2 × 4 + 4√2

Or, Perimeter = 8 + 4√2  cm

So, The perimeter of isosceles right Triangle = P = 8 + 4√2  cm

Hence, The perimeter of isosceles right Triangle is 8 + 4√2  cm Answer

Answer 2

HOPE THIS HELPS YOU

Step-by-step explanation:

WE KNOW THAT:

For isosceles right Triangle

The Area of isosceles right Triangle = A = 8 sq cm

Let , The measure of common side = a cm

The measure of uncommon side = h cm

Let The perimeter of isosceles right Triangle = P cm

According to question

Area =  × base × height

i.e base × height = 2 × A

Or, base × height = 2 × 8

Or, b × b = 16 sq cm

i.e  b × b = 16 sq cm

Or,  b² =  16

i.e  b = √16 = 4 cm

So, measure of common side = b = 4 cm h = 4√2 cm

So, measure of THIRD  side = h = 4√2  cm

perimeter of isosceles right Triangle = ( 2 b + h ) cm

i.e P = 2 × 4 + 4√2

Or, Perimeter = 8 + 4√2  cm