# One side of an isosceles triangle whose perimeter is 42 units measures 10 units. find the area of the triangle

2
by princessaurora

2015-11-21T22:50:39+08:00

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I think 76 square units. :)
Hahah. P= 2a + b so 42= 2(10) + b. 42=20+b then I transposed 20 it becomes 42-20=b. 22=b and that's my base. then I go the altitude by a=√10^2-11^2/4 and I got 8.35 as its altitude then I used the A= 1/2 bh hahaha. Just sharing what I did.
Try again, haha :-) You were on the right track but detoured. Assigning 22 as base is not possible. Since altitude is perpendicular to the base, therefore, with 11 (22/2) as base and 10 as the hypotenuse, then you'll get a negative altitude using the pythagorean theorem for right triangle. Keep doing what you're doing, investigating by solving. Very smart :-) Eventually, solving will be a lot easier.
I think I got it , Try to check this. 42=2a+10 I used 10 as my base a= 42-10/2 a=16 then to get the height √16^2-5^2 h=√231. I used the A= 1/2 (10)(√231) and I got 76
I think I got it , Try to check this. 42=2a+10 I used 10 as my base a= 42-10/2 a=16 then to get the height √16^2-5^2 h=√231. I used the A= 1/2 (10)(√231) and I got 76
That's correct :-)
• Brainly User
2015-11-24T11:35:53+08:00
Given the  equal legs with measurement of 16 units each, and base with length of 10 units, the altitude/height is computed using the Pythagorean theorem because the altitude perpendicular to the base divides the isosceles triangle into two congruent right triangles.

(Height)² = (16)² - (10/2)²
(Height)² = 256 - 25

Area of the triangle = (bh)/2

Area = [(10)] ÷ 2

Area = 10√231
2

Area = 5√231

Area ≈ 5 (15.19868)

Area ≈ 75.9934

Area ≈ 76 sq. units

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