college algebra

posted by .

if the altitude and the base of a triangle are each increased by 4 inches the area of the triangle will be increased by 42 square inches. if the altitude is increased by 3 inches and the base is decreased by 2 inches the area will be increased by 5 square inches. find the base and the altitude of the triangle.

  • college algebra -

    let original base be b and height be h

    original area = bh/2

    case1:
    new base = b+4
    new height = h+4
    new area = (b+4)(h+4)/2 = bh/2 + 42
    bh + 4b + 4h + 16 = bh + 84
    4b + 4h = 68
    b+h = 17 #1

    case2:
    new base = b-2
    new height = h+3
    new area = (b-2)(h+3)/2 = bh/2 + 5
    bh + 3b - 2h - 6 = bh + 10
    3b - 2h = 16 #2

    #1 x 2 ---->2b+2h= 34
    add to #2
    5b = 50
    b = 10
    a = 7

    original base is 10 inches
    original height is 7 inches

    check:
    original area = 35
    case1:
    area = 14(11)/2 = 77 , it increased by 42
    case2:
    area = (10)(8)/2 = 40 , it increased by 5

    all is good!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    The area A of a triangle is given by the formula A=1/2bh If the base of the triangle with height 12 inches is doubled, its area will be increased by 48 square inches. Find the base of the orignial triangle.
  2. Math

    The area A of a triangle is given by the formula A=1/2bh If the base of the triangle with height 12 inches is doubled, its area will be increased by 48 square inches. Find the base of the orignial triangle.
  3. algebra 1

    The area of trapezoid is h( b1+b2)/5, where h is the altitude, and b1 and b2 are the lenghts of the parallel bases. If trapezoid has an altitude of 5 inches, an area of 55 square inches , and one base 12 inches long, what is the lenghth, …
  4. math

    The area of trapezoid is h( b1+b2)/5,where h is the altitude, and b1 and b2 are the lenghts of the parallel bases. If trapezoid has an altitude of 5 inches, an area of 55 square inches , and one base 12 inches long, what is the length, …
  5. math

    The area of trapezoid is h( b1+b2)/5,where h is the altitude, and b1 and b2 are the lenghts of the parallel bases. If trapezoid has an altitude of 5 inches, an area of 55 square inches , and one base 12 inches long, what is the length, …
  6. Math

    The area of trapezoid is h( b1+b2)/5, where h is the altitude, and b1 and b2 are the lenghts of the parallel bases. If trapezoid has an altitude of 5 inches, an area of 55 square inches , and one base 12 inches long, what is the lenghth, …
  7. math

    an altitude of triangle is 5/3rd of the length of its corresponding base if their altitude be increased by 4cm and the base is decreased by 2cm, the area of the triangles remain the same. find the base and altitude of triangle ?
  8. math

    If each edge of a cube is increased by 2 inches, the A. volume is increased by 8 cubic inches B. area of each face is increased by 4 square inches D. sum of the edges is increased by 24 inches
  9. Math

    The base of a triangle is three inches more than its height. If each is increased by 3 inches the area of the triangle (1/2 bh) is 14 square inches. Find the original base (𝑏) and the original height (ℎ) in inches. (Lesson …
  10. Math

    The base of a triangle is three inches more than its height. If each is increased by 3 inches the area of the triangle (1/2 bh) is 14 square inches. Find the original base (𝑏) and the original height (ℎ) in inches. (Lesson …

More Similar Questions