Question

the perimeter of a rectangle is 38 meters and it's area is 78 square meters. find the length and the width of the rectangle​

Answer 1

Answer:

length of rectangle 13m

breadth of rectangle 6m

Answer 2

Length = 6 or 13 and Width = 13 or 6.

Explanation:

Given: Perimeter of a rectangle = 38, Area = 78 square meters.

To Find: Length, Width.

Solution:

• Perimeter is defined as the total measurement of an shape with all the edges.

• Perimeter of an rectangle:   $2 ( L +W) = 38$   ;   $L +W = 19$.
• Where, $W = 19 - L$.
• Area is defined as the space that are occupied by an surface.
• A = L × W    ;    $LW = 78$ .
• Substituting W in Area, $L (19 - L) = 78$    ;    $19L - L^{2} - 78 =0$ .
• Multiplying with ( - ) sign we get, $L^{2} -19L+78 = 0$.
• Solving the above equation, $( L - 6)$ $( L - 13 )$    ;   L = 6 or 13.
• Substituting the Value of L in $W=19-L$ we get, W = 13 or 6.
• Hence L = 6 and W = 13 ( or ) L = 13 and W = 6.