Find the base of an isoscles triangle whose area is 60cm sq. And the length of one of its equal side is 13 cm. Using formula of isoscles triangle i. e. b/4√4a^2-b^2. Only by this method
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Answer:
The length of one of the equal sides is 13 cm and the area of the isosceles triangle is 60 sq cm.
If you see the Pythagorean triplets, a hypotenuse of 13 units will have the other two sides as 5 and 12. From this you can see there are two possibilities:
(1) base of right-angled triangle is 12 cm and the height 5 cm. This gives the area as 12*5/2 = 30 sq cm. And the isosceles triangle which is the mirror image of the right-angled triangle about the vertical side has a base of 24 cm and its height is 5 cm. The area of the isosceles triangle = 24 *5/2 = 60 sq cm.
(2) base of right-angled triangle is 5 cm and the height 12 cm. This gives the area as 5*12/2 = 30 sq cm. And the isosceles triangle again which is the mirror image of the right-angled triangle about the vertical side has a base of 10 cm and its height is 12 cm. The area of the isosceles triangle = 10 *12/2 = 60 sq cm.
Thus the isosceles triangle can have (1) a base of 24 cm and height of 5 cm or (2) a base of 10 cm and height of 12 cm.