How can I find the base of an isoceles triangle when I only know the area is 24 square feet and the legs are 8ft. I need to find the base.
by 
Kikironi
ANSWERS: 5
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Try to picture this in another way. Since you have an isoceles triangle, you can move the triangle to have a right triangle, still a isoceles triangle, since both of your legs are 8ft long. The formula is this- A= 1/2BH Your problem is... 24=1/2xBx8ft Multiply 1/2 by 2. This will equal 1, which can be negated. Now multiply 24 by 2, making it 48. Then divide 8 by 8 to become 1, to negate it. Now deivide 48/8. This should equal 6. Your final answer is 6ft for the base.
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If I understand what you're asking, this is not as easy as it looks. Being an isoceles triangle, it's symmetrical. Fold the triangle in half. Then you have a right triangle with area = 12 square feet and hypotenuse 8 feet, height h, and base b. h^2 + b^2 = 64 from pythagoras and (hb)/2 = 12 from the formula for the area of the triangle. multiply that by four: 2hb = 48 Add the 2hb to the first equation h^2 + 2hb + b^2 = 112 (h+b)^2 = 112 h+b = sqrt(112) = 10.583 Or subtract the 2hb from the first equation: h^2 - 2hb + b^2 = 16 h-b = plus or minus 4 Subtract those two results 2b = 10.583 plus or minus 4 (to three decimal places) And 2b is the base of the original unfolded triangle. Check: If 2b = 14.583 then b = 7.2915 and h = 3.2915 b^2 + h^2 = 64 b*h = 24 If 2b = 6.583 then b = 3.2915 and h = 7.2915 and the check is the same as the formula are symmetrical.
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Ask him?
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One could use Heron's formula: If the sides of a triangle are labelled a, b & c and S = (a+b+c)/2 then the area of the triangle = [S(S-a)(S-b)(S-c)]^.5 In this case: Area = 24 S = (a+8+8)/2 = (a+16)/2 = 8+a/2 a = unknown b = 8 c = 8 24 = [(8+a/2)(8+a/2-a)(8+a/2-8)(8+a/2-8)]^.5 576 = (8+a/2)(8-a/2)(a/2)(a/2) = (64-(a/2)^2)(a/2)^2 (a/2)^2 = u 576 = u(64-u) 0 = -u^2 + 64u - 576 Using the quadratic formula we get u = (-64 +/- (64^2 - 4*(-1)*(-576))^.5)/(2*(-1)) = (-64 +/- (4096 - 2304)^.5)/(-2) = (-64 +/- 1792^.5)/(-2) = (64 + 42.33202098)/2 & u ~= (64 - 42.33202098)/2 u ~= 53.16601049 & u = 10.83398951 (a/2)^2 ~= 53.16601049 a/2 ~= 7.291502622 a ~= 14.58300524 Also (a/2)^2 ~= 10.83398951 a/2 ~= 3.291502622 a ~= 6.583005244 Just to double check: Area of a triangle = B*H/2 a^2 + b^2 = c^2 H = (8^2 - B^2)^.5 C ~= 14.58300524 Area of traingle = (C*(8^2-(C/2)^2)^.5)/2 = 24 D ~= 6.583005244 Area of traingle = (D*(8^2-(D/2)^2)^.5)/2 = 24
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Without Formula? You would have to take the measurement of a smaller triangle and do it by ratio's. meaning draw two three inch legs on a ninety degree angle and measure the base. Then multiply the base in the scale drawing by 8. I am not good while I am working at remembering formula's but I can always do this.
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