Question

Find the base of an isosceles triangle whose area is 60 sq. cm and length of equal side is 13 cm.

Answer 1

Hi ...dear.
here is your answer..
..24 or.10.....
hope this will help you..!!
Regards Brainly Star Community
#shubhendu

Answer 2

Answer:

24cm or 10cm

Step-by-step explanation:

Given:- Area of an Isosceles triangle = 60 sq. cm

            Length of the equal sides = 13 cm.

To Find:- Base of the isosceles triangle.

Solution:-

An isosceles triangle is a triangle whose two sides are of equal length and those two sides join to the base i.e. the third side at the equal angle.

As we know, Area of an Isosceles triangle = 1/2 × Base × Height

Let the two equal sides be denoted by a, base be 2b and height be h.

∴ Area = 1/2 × b × h

As we know, the height divides the triangle into two right angle triangle.

∴ h = $\sqrt{ a^{2} - b^{2} }$  [ ∵ perpendicular = $\sqrt{hypotenuse^{2} - base^{2} }$]

∴ Area = 1/2 × 2b × $\sqrt{ a^{2} - b^{2} }$

⇒ 60 = 1/2 × 2b × $\sqrt{ (13)^{2} - b^{2} }$

⇒ 60 = b × $\sqrt{ (13)^{2} - b^{2} }$

⇒ 3600 = $b^{2} (169 - b^{2} )$

⇒ $(b^{2} -144)(b^{2} -25) =0$

⇒ $b^{2}$ = 144, 25.

∴ b = 12, 5

∴ Base = 2 × 12 = 24 cm or 5 × 2 = 10 cm.

Therefore base of the isosceles triangle is either 24cm or 10cm.

#SPJ3

What is an Isosceles triangle, click here

https://brainly.in/question/242761

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https://brainly.in/question/6258851