The length of a hypotenuse of a right triangle exceeds the length of its base by 2cm and exceed twice the length of the altitude by 1cm .Find the length of each side of the triangle (in cm)

Answer

base = 15 cm, altitude = 8 cm , hypotenuse = 17 cm

Explanation

Let the base be x cm. Then, hypotenuse `=(x+2)cm.`
`(x+2)-(2xx"altitude")=1implies2xx" altitude"=(x+1)`
`implies" altitude "=(1)/(2)(x+1)cm.`
`:." "(x+2)^(2)=x^(2)+(1)/(4)(x+1)^(2)implies4(x+2)^(2)=4x^(2)+(x+1)^(2)`
`implies" "4(x^(2)+4x+4)=5x^(2)+2x+1impliesx^(2)-14x-15=0`
`implies" "(x-15)(x+1)=0impliesx=15.`