# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४१७

एतत् पृष्ठम् परिष्कृतम् अस्ति
221
CHAPTER VII--MEASUREMENT OF AREAS.

of the said optionally chosen 'figure happens to be arrived at); or the base (of such an optionally chosen figure of the requisite type), on being multiplied by the factor with which the area (of the said figure) has to be multiplied (to give the required kind of result); gives rise to the measures of the bases of the (required) equilateral quadrilateral and other kinds of derived figures.

Examples in illustration thereof.

113${\displaystyle {\tfrac {1}{2}}}$. In the case of an equilateral quadrilateral figure, the (numerical measure of the) perimeter is equal to (that of) the area. What then is the numerical measure of (its) base ? In the case of another (similar) figure, the (numerical) measure of the area is equal to (that of) the base. Tell me in relation to that (figure) also (the numerical measure of the base).

114${\displaystyle {\tfrac {1}{2}}}$. In the case of an equilateral quadrilateral figure, the (numerical) measure of the diagonal is equal to (that of) the area. What may be the measure of (its) base ? And in the case of another (similar) figure, the (numerical) measure of the perimeter is twice that of the area. Tell me (what may be the measure of its base).

115${\displaystyle {\tfrac {1}{2}}}$. Here in the case of a longish quadrilateral figure, the (numerical) measure of the area is equal to that of the perimeter; and in the case of another (similar) figure, the (numerical) measure of the area is equal to that of the diagonal. What is the measure of the base (in each of these cases)?

116${\displaystyle {\tfrac {1}{2}}}$. In the case of a certain equilateral quadrilateral figure, the (numerical) measure of the base is three times that of the area. (In the case of) another equilateral quadrilateral figure, the (numerical) measure of the diagonal is four times that of the area. What is the measure of the base (in each of these cases) ?

the measure of the perimeter, viz. 20, has to be multiplied in order to make it equal to the measure of the area, viz., 25, is ${\displaystyle {\tfrac {5}{4}}}$. If 5, the measure of a side of the optionally chosen quadrilateral is divided by this factor 4, the measure of the side of the required quadrilateral is arrived at.

The rule gives also in another manner what is practically the same process thus: The factor with which the measure of the area, viz. 25 has to be multiplied in order to make it equal to the measure of the perimeter, viz. 20, is ${\displaystyle {\tfrac {4}{5}}}$. lf 5, the measure of a side of the optionally chosen figure is multiplied by this factor , the measure of the side of the required figure is arrived at.