ABC is a right triangle .b is right angle. Ab is 7 units more than BC if area of a triangle is 60 square units find the length of ab and BC

Question

ABC is a right triangle .b is right angle. Ab is 7 units more than BC if area of a triangle is 60 square units find the length of ab and BC and the length of AC

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Claire 2 weeks 2021-11-24T21:52:27+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-24T21:53:43+00:00

    GIVEN:

    • AB is 7 units more than BC.
    • Area of the triangle is 60 sq. units.

    TO FIND:

    • What is the length of AB, BC and AC ?

    SOLUTION:

    Let the side BC be ‘x’ units

    We have given that, AB is 7 units more than BC.

    So, let side AB be ‘x + 7 units

    To find the area of the triangle, we use the formula:-

    ❮ AREA = \bf{\dfrac{1}{2} \times b \times h} ❯ 

    According to question:

    ➸ 60 = \sf{\dfrac{1}{2} \times x \times x + 7}

    60 \times 2 = x² + 7x

    120 = x² + 7x

    0 = x² + 7x –120

    0 = x² + (15–8)x –120

    0 = x² + 15x –8x –120

    0 = x(x + 15) –8(x + 15)

    0 = (x –8)(x + 15)

    x = 15 ❱ (Neglected)

    ❰ x = 8 ❱

    • x = BC = 8 units
    • x + 7 = AB = 8+7 = 15 units

    To find the length of AC, we apply the Pythagoras theorem

    ⠀⠀ ❰ H² = P² + B² ❱

    Where,

    • H = Hypotenuse
    • P = Perpendicular
    • B = Base

    According to question:

    ➨  (AC)² = (AB)² + (BC)²

    AC² = 15² + 8²

    AC² = 225 + 64

    AC² = 289

    AC = √289

    AC = 17 units ❭ 

    Hence, the length of AB, BC and AC is 15, 8 and 17 units respectively.

    ______________________

    0
    2021-11-24T21:54:21+00:00

    Answer:

    LET BC BE X AND AB= X+7

    SO area of rt angle triangle = 1/2 * product of legs=

    here 1/2 * x* (x+7)= 60

    on simplifying, we get, x^2 + 7x- 120= 0

    quadratic so, (x-8)(x+15)= 0

    so x= -15 or 8 length isnt -ve

    AB =8 & BC= 15

    BY PYTHAGORAS THEOREM, AC = 17 ‘

    PLS MARK BRAINLIEST

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