Question

the lengths of the parallel sides of a trapezium are in the ratio 4 :7 if the height of a trapezium is 49 and its area is 385 sq m find the length of its parallel side​

Answer 1

${\large{\pmb{\sf{\underline{Understanding \; the \; question...}}}}}$

◆ This question says that we have to find out the length of the parallel sides of a trapeizum whose area is 385 metres sq. And the lengths of the parallel sides of a trapezium are in the ratio 4:7 The height of the trapezium is 49 metres. Let's solve this question properly!

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

• A trapezium is given.
• Parallel side of the trapezium is given as in the ratio of 4:7 respectively.
• Height = 49 metres
• Area = 385 metres sq.

${\large{\pmb{\sf{\underline{To \: find...}}}}}$

• Length of both the parallel sides of the given trapezium.

${\large{\pmb{\sf{\underline{Solution...}}}}}$

• Length of both the parallel sides of the given trapezium are 5.68 m and 9.94 metres respectively

${\large{\pmb{\sf{\underline{Assumptions...}}}}}$

• a is the common ratio.

• Let 4a and 7a are the parallel sides of the given trapezium respectively.

${\large{\pmb{\sf{\underline{Using \; formula...}}}}}$

${\quad \quad \quad{\pmb{\sf{\circ \: \: Area \: of \: trapezium \: formula...}}}}$

${\small{\underline{\boxed{\sf{\dfrac{1}{2} \times (a+b) \times height}}}}}$

• [Here a and b are the parallel sides of the given trapezium].

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ To sove this question firstly we have to find out the value of a(common ratio). We have to find out by using the formula to find out the area of trapezium we just have to put the values according to the formula and we get value of a.

${\small{\underline{\boxed{\sf{Area \: = \dfrac{1}{2} \times (a+b) \times height}}}}}$

${\sf{:\implies Area \: = \dfrac{1}{2} \times (a+b) \times height}}$

${\sf{:\implies 385 \: = \dfrac{1}{2} \times (4a+7a) \times 49}}$

${\sf{:\implies 385 \: = \dfrac{1}{2} \times (11a) \times 49}}$

${\sf{:\implies 385 \: = \dfrac{539a}{2}}}$

${\sf{:\implies 385 \: = 269.5a}}$

${\sf{:\implies \dfrac{385}{269.5} = a}}$

${\sf{:\implies 1.42 = a}}$

${\sf{:\implies a = \: 1.42 \: m}}$

• Henceforth, common ratio i.e., is 1.42 metres.

~ Now just find the length of both the parallel sides of the given trapezium.

${\quad \quad \quad{\pmb{\sf{\circ \: \: First \: parallel \: side...}}}}$

${\sf{:\implies 4a}}$

${\sf{:\implies 4(1.42)}}$

${\sf{:\implies 4 \times 1.42}}$

${\sf{:\implies 5.68 \: metres}}$

• Henceforth, first parallel side is 5.68 metres.

${\quad \quad \quad{\pmb{\sf{\circ \: \: Second \: parallel \: side...}}}}$

${\sf{:\implies 7a}}$

${\sf{:\implies 7(1.42)}}$

${\sf{:\implies 7 \times 1.42}}$

${\sf{:\implies 9.94 \: metres}}$

• Henceforth, second parallel side is 9.94 metres.