Maths-
General
Easy

Question

Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z

Hint:

Applying the property of a rectangle equates the lengths of opposite sides of the rectangle .

The correct answer is: y=12 and z=8


    Ans :- y = 12 and z = 8
    Explanation :-
    Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm.
    Step 1:- form the system of linear equations using the given condition
    AB = CD (opposite sides of the rectangle are equal.)
    4 y minus z equals 2 y plus z plus 8 not stretchy rightwards double arrow 2 y equals 2 z plus 8
    not stretchy rightwards double arrow y equals z plus 4 — Eq1
    BC = DA(opposite sides of the rectangle are equal.)
    not stretchy rightwards double arrow y plus 4 equals 2 z — Eq2
    Step 2:- substitute the Eq1 in Eq2.
    not stretchy rightwards double arrow y plus 4 equals 2 z not stretchy rightwards double arrow left parenthesis z plus 4 right parenthesis plus 4 equals 2 z
    not stretchy rightwards double arrow z plus 8 equals 2 z
    not stretchy rightwards double arrow 8 equals z
    ∴ z = 8
    Step 3:- the value of z in Eq1.
    not stretchy rightwards double arrow y equals z plus 4 not stretchy rightwards double arrow y equals 8 plus 4
    not stretchy rightwards double arrow y equals 12
    ∴ y = 12

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