Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 241: 30

By what we learned in this section, and by using the pythagorean theorem we could find the altitude. Step 1 : let “ b “ be the altitude, and since b separates the hypotenuse into two unequal parts, let’s name one as “ x” and the second as “ y “ for facility. Step 2 : b separates the original triangle into two similar triangles with legs 6 and 8 inches and the hypotenuse is 10 in. Step 3 : apply pythagorean theorem in triangle 1 $6^{2}=b^{2} + x^{2}$, and apply the same theorem in the second triangle therefore $8^{2}= b^{2}+ y^{2}$. Step 4 : since x + y = 10 then x= 10-y. Substitute x in the step two and evaluate it . We obtain $36= b^{2}+ 10^{2}-20y+y^{2}$. $y^{2}+ b^{2}+64-20y = 0$. Step 4 : create a system of equation between $y^{2}+ b^{2}+64-20y = 0$ $b^{2}+ y^{2} - 64=0$ Step 5 : by subtraction we conclude 128-20y=0 Therefore y= 6.4 Step 6: by substituting y in one of the equations in Step 4 we obtain that b= height= 4.8.

Work Step by Step

I used the equation for altitude to find this value.

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