SOLUTION: "The base of a triangle is x cm long and its altitude is quarter the length of its base. If the triangle has an area of 12 cm^2, from an equation in x and solve it. State the altit

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: "The base of a triangle is x cm long and its altitude is quarter the length of its base. If the triangle has an area of 12 cm^2, from an equation in x and solve it. State the altit      Log On


   

Question 1151122: "The base of a triangle is x cm long and its altitude is quarter the length of its base. If the triangle has an area of 12 cm^2, from an equation in x and solve it. State the altitude of the triangle."










The length of a parallelogram is d cm and its altitude is 3 cm shorter. The side of a square is shorter by a further 2 cm. If the sum of the areas of the parallelogram and square is 95 cm^2, prove the 2d^ - 13d -70=0. Hence find the length oh the parallelogram in centimeters.








Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The base of a triangle is x cm long and its altitude is quarter=1%2F4 the length of its base.
then the length of its altitude is a=%281%2F4%29x
If the triangle has an area of 12+cm%5E2, from an equation in x and solve it.
A=%281%2F2%29base%2Aaltitude
12=%281%2F2%29x%2A%281%2F4%29x
12=%281%2F8%29x%5E2
12%2A8=x%5E2
96=x%5E2
x=sqrt%2896%29
x=4sqrt%286%29%E2%80%ADcm%E2%80%AC-> exact solution
x=9.8%E2%80%ADcm%E2%80%AC-> approximate solution
the altitude of the triangle is:
a=%281%2F4%29x=>a=%281%2F4%294sqrt%286%29=>a=sqrt%286%29-> exact solution




2.
The length of a parallelogram is d cm and its altitude is 3 cm shorter.
altitude is d-3
The side of a square is shorter by a further 2 cm=> The side of a square is d-5
If the sum of the areas of the parallelogram and square is 95cm^2, prove the 2d%5E2+-+13d+-70=0:
%28d-5%29%5E2%2Bd%28d-3%29=95
d%5E2-10d%2B25%2Bd%5E2-3d=95
2d%5E2-13d%2B25-95=0
2d%5E2-13d-70=0...to find d use quadratic formula


d=%28-%28-13%29%2B-sqrt%28%28-13%29%5E2-4%2A2%2A%28-70%29%29%29%2F%282%2A2%29
d=%2813%2B-sqrt%28169%2B560%29%29%2F4

d=%2813%2B-sqrt%28729%29%29%2F4
d=%2813%2B-27%29%2F4-> since looking for the length oh the parallelogram, disregard negative solution
d=%2813%2B27%29%2F4
d=40%2F4
d=10
find the length oh the parallelogram is 10 centimeters
check the areas:
length of a parallelogram is d=10 cm and its altitude is d-3=10-3=7cm
d%28d-3%29=10%2A7=70
The side of a square is d-5=10-5=5 cm, and area is
%28d-5%29%5E2=%2810-5%29%5E2=5%5E2=25
the sum of the areas of the parallelogram and square is 70%2B25=95 which confirms our solution