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vovikov84 [41]
3 years ago
5

One leg of a right triangle is 7 inches longer than the smaller leg and the hypotenuse is 8 inches longer than the smaller leg.

Find the lengths ofl the side
of the triangle
Mathematics
1 answer:
Makovka662 [10]3 years ago
3 0
Smaller leg = x
longer leg = y
hypotenuse = z

y=x+7
z=x+8

due to
{z}^{2}  =  {x}^{2}  +  {y}^{2}  \\ (x + 8) ^{2}  =  {x}^{2}  + (x + 7) ^{2}  \\  {x}^{2}  + 16x + 64 =  {x}^{2}  +  {x}^{2}  + 14x + 49 \\  {x}^{2}  + 16x + 64 = 2 {x}^{2}  + 14x + 49 \\  {x}^{2}  - 2 {x}^{2}  + 16x - 14x + 64 - 49 = 0 \\  -  {x}^{2}  + 2x + 15 = 0 \\  {x}^{2}  - 2x - 15 = 0 \:  \: (multiplied \: by \:  - 1) \\ (x - 5)(x + 3) = 0 \\ then \:  \: x = 5 \:  \: or \:  \: x =  - 3
but x cannot be -3
so smaller leg is 5 inches

then longer leg = 5+7 = 12 inches
and hypotenuse = 5+8 = 13 inches
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