Question

The difference between the sides at right angles in a right-angled
triangle is 14 cm. The area of the triangle is 120 cmº. Calculate the
perimeter of the triangle​

Answer 1

Answer:

... is 14 cm. The area of the triangle is 120 cm ^ 2 . ... Let the sides at right angles in the given right-angled triangle be a and b. Without loss ...

Missing: cmº. ‎| Must

Step-by-step explanation:

... is 14 cm. The area of the triangle is 120 cm ^ 2 . ... Let the sides at right angles in the given right-angled triangle be a and b. Without loss ...

Missing: cmº. ‎| Must

Answer 2

Given

• Difference between the sides at right angles in a right-angled triangle is 14 cm
• Area of the triangle = 120cm²

Explanation

FORMULA

$\maltese {\boxed{\underline{\sf{ Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height }}}}$

Let the sides containing right angle be x and (x - 14)

Then, Area be like ${\sf{ \dfrac{1}{2} \times x \times (x-14) }}$

According to Question,

$\colon\implies{\sf{ 120 = \dfrac{1}{2} \times x \times (x-14) }} \\ \\ \\ \colon\implies{\sf{ 120 \times 2 = x (x-14) }} \\ \\ \\ \colon\implies{\sf{ 240 = x^2 - 14x }} \\ \\ \\ \colon\implies{\sf{ x^2 - 14x - 240 = 0 }} \\ \\ \\ \colon\implies{\sf{ x^2 -(24-10)x-240 = 0 }} \\ \\ \\ \colon\implies{\sf{ x^2 - 24x +10x-240 = 0 }} \\ \\ \\ \colon\implies{\sf{ x(x-24)+10(x-24) = 0 }} \\ \\ \\ \colon\implies{\sf{ (x-24)(x+10)=0 }} \\ \\ \\ \colon\implies{\sf{ x= 24 \ \ and \ \ -10 }}$

Side Can't be Negative ( -ve ).

So, Sides be :-

• x = 24 cm
• (x - 10) = (24 - 14) = 10 cm

$\maltese$ Now, We have to find the third Side which is diagonal :-

We can use Pythagoras theorem to find third side as,

$\colon\implies{\sf{ h^2 = b^2 + p^2}} \\ \\ \colon\implies{\sf{ h^2 = (24)^2 + (10)^2 }} \\ \\ \colon\implies{\sf{ h^2 = 576 + 100 }} \\ \\ \colon\implies{\sf{ h^2 = 676 }} \\ \\ \colon\implies{\sf{ h = \sqrt{676} }} \\ \\ \colon\implies{\sf\large\red{ h = 26 \ cm \ \ \ \ \ \sf\purple{(Diagonal)} }}$

$\maltese$ Now Finally, We can find Perimeter of the Triangle as :-

• Three sides are 24cm, 10cm, 26cm

$\maltese {\boxed{\sf\gray{ Perimeter_{( \Delta )} = a + b + c }}} \\ \\ \\ \colon\implies{\sf{ Perimeter_{( \Delta )} = 24 + 10+26 }} \\ \\ \\ \colon\implies{\boxed{\sf\green{ Perimeter_{( \Delta )} = 60 \ cm }}}$

Hence,

• The Perimeter of the Triangle is 60 cm.