Question

The area of a trapezium is 72 cm2 and its height is 12
cm. If one of the parallel sides is longer than the
other by 2 cm, find the sum of the length of two
parallel sides.​

Answer 1

$\huge\mathtt{\underline{ANSWER:-}}$

7cm and 5 cm

$\huge\mathbb{\underline{\underline{SOLUTION:-}}}$

$\bold{Given}\begin{cases}\sf{Area\:of\: trapezium=72cm{}^{2}}\\ \sf{height=12cm}\\ \sf{one \:of \:its\: parallel\:side\:is\: longer\:to\:other\:by\:2cm}\end{cases}$

$\huge\bold{To \:Find:-}$

The parallel sides of trapezium

$\bold{\red{According\:to\: question}}$

$\sf Area\:of\: trapezium=\frac{1}{2}\times Height\times (sum\:of\: parallel\:sides)$

let it's parallel sides be x and other is x+2

Now:-

$\sf Area=\frac{1}{2}\times Height\times (sum\:of\: parallel\:sides)\\ \\ \sf\leadsto 72=\frac{1}{2}\times 12\times (x+x+2)\\ \\ \sf\leadsto 72\times 2=12\times 2x+2\\ \\ \sf\leadsto \cancel{\frac{144}{12}}=2x+2\\ \\ \sf\leadsto 12-2=2x\\ \\ \sf\leadsto \cancel{\frac{10}{2}}=x\\ \\ \sf\leadsto 5=x$

The value of x is 5

means it's one parallel side is 5 and other is 5+2

=7

Now verify our answer to check it is correct or not

if it's correct it will L.H.S=R.H.S

$\sf Area\:of\: trapezium=\frac{1}{2}\times Height\times (sum\:of\: parallel\: sides)\\ \\ \sf\leadsto 72=\frac{1}{\cancel 2}\times \cancel{12}\times (5+7)\\ \\ \sf\leadsto 72= 6\times12\\ \\ \sf\implies 72=72$

L.H.S=R.H.S

$\boxed{\blue{\bold{parallel\:sides=5cmand 7cm}}}$

#BAL

#AnswerwithQuality

Answer 2

Answer:

Step-by-step explanation: